For seven years I've been trying to discuss monetary policy, and commenters (mostly at MoneyIllusion) keep wanting to bring up a completely unrelated topic---banking. Monetary policy works though the hot potato effect, and banking is no more essential to the transmission mechanism than is the auto parts industry. Print more currency than people want to hold and NGDP gets forced higher---that's monetary economics.
Over the past decade the central bank that boosted NGDP the most was in Zimbabwe. Here's a picture showing someone shopping for pants in 2006.
Banks played no role in the hyperinflation---you could have destroyed the entire Zimbabwe banking industry with a neutron bomb, and printing that much currency would still have led to hyperinflation. You print more currency than the public wants to hold, and they'll bid up prices. How do you inject it without banks? Simple, pay government worker salaries in cash. Or buy T-bonds for cash. Cantillon effects don't matter, unless the central bank is doing something bizarre, like buying bananas. A budget deficit isn't essential either. Zimbabwe did finance its deficit by printing money, but you could just as easily create hyperinflation with a budget surplus. A quadrillion Zimbabwe dollars will do wonders for NGDP, regardless of what else is going on.
Some commenters keep insisting that "banks don't lend out reserves." That's only true in the sense that "customers can never leave Walmart or Target." If banks lend someone money, and they withdraw the funds in cash, it's no longer called "reserves." But that's like saying a customer can never leave Target because if they left the store they no longer be a customer---they'd be a pedestrian.
Others say banks can't control the aggregate amount of reserves. Sure they can; they simply lower the interest rate on deposits (or if the rate is already zero then raise the service fee) and the public will choose to hold more cash. If you made the interest rate on reserves negative 3% then almost all of the reserves would pour out of the banking system and be held as cash. In the US (in 2015) that would lead to hyperinflation, whereas in the US in 2009 or in Japan today it might lead to hyperinflation, or it might lead to lots of cash being stored in safety deposit boxes.
Negative interest on reserves is certainly not a first best policy; NGDP level targeting is far better. But if central banks really are refraining from doing the appropriate amount of monetary stimulus due to fear of an excessively large balance sheet, then negative IOR is a good way of reducing that balance sheet. But don't make it negative 1/4%, do something that matters---negative 3%.
PS. Just to be clear, cash in safety deposit boxes is considered to be cash in circulation, not bank reserves. Vault cash owned by banks is part of bank reserves.